Simple Interest
Math MCQs

Question :    Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 9% simple interest.

Correct Answer  $10355

Solution & Explanation

Solution

Given,

Principal (P) = $5450

Rate of Simple Interest (SI) = 9%

Time (t) = 10 years

Thus, Amount (A) = ?

The Rate of Interest is always calculated per annum, i.e. per year.

Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% per annum.

Method (1) Using Formula

Calculation of Simple Interest

Formula to Calculate Simple Interest

Simple Interest (SI) = Principal × Rate × Time

Thus, Simple Interest (SI) = $5450 × 9% × 10

= $5450 ×⁹/₁₀₀ × 10

= ^{5450 × 9 × 10}/₁₀₀

= ^{49050 × 10}/₁₀₀

= ⁴⁹⁰⁵⁰⁰/₁₀₀

= $4905

Thus, Simple Interest = $4905

Calculation of Amount

The total money paid to the lender by a borrower is called the Amount.

In other words, sum of priciple and interest is called the Amount.

Formula to Calculate the Amount

Amount = Principal + Interest

Thus, Amount = $5450 + $4905

= $10355

Thus, Amount to be paid = $10355 Answer

Method (2)

Calculation of Amount when Principal, Rate of Simple Interest and Time are given

Calculation of Amount directly using Principal, SI, and Time

Formula to calculate the Amount

Amount (A) = Principal (P) + Principal(P) × Rate of Interest (SI) × Time (t)

⇒ A = P + PRT

Here in the question, P = $5450

Rate of Simple Interest (SI) or (R) = 9%

And, Time (t) = 10 years

Thus, Amount (A)

= $5450 + ($5450 × 9% × 10)

= $5450 + ($5450 ×⁹/₁₀₀ × 10)

= $5450 + (^{5450 × 9 × 10}/₁₀₀)

= $5450 + (^{49050 × 10}/₁₀₀)

= $5450 + (⁴⁹⁰⁵⁰⁰/₁₀₀)

= $5450 + $4905 = $10355

Thus, Amount (A) to be paid = $10355 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 9%

This, means, $9 per $100 per year

∵ For $100, the simple interest for 1 year = $9

∴ For $1, the simple interest for 1 year = ⁹/₁₀₀

∴ For $5450, the simple interest in 1 year

= ⁹/₁₀₀ × 5450

= ^{9 × 5450}/₁₀₀

= ⁴⁹⁰⁵⁰/₁₀₀ = $490.5

Thus, simple interest for 1 year = $490.5

Therefore, simple interest for 10 years

= Simple interest for 1 year × 10

= $490.5 × 10 = $4905

Thus, Simple Interest (SI) = $4905

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5450 + $4905

= $10355

Thus, Amount to be paid = $10355 Answer

Similar Questions

(1) Find the amount to be paid if Mary borrowed a sum of $5050 at 5% simple interest for 8 years.

(2) If Jessica paid $4050 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(3) How much loan did Melissa borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8452.5 to clear it?

(4) In how much time a principal of $3100 will amount to $3224 at a simple interest of 2% per annum?

(5) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 9% simple interest.

(6) Calculate the amount due if Jennifer borrowed a sum of $3250 at 8% simple interest for 3 years.

(7) How much loan did Lisa borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7562.5 to clear it?

(8) Calculate the amount due if Thomas borrowed a sum of $3800 at 8% simple interest for 4 years.

(9) In how much time a principal of $3200 will amount to $4000 at a simple interest of 5% per annum?

(10) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $5680 to clear the loan, then find the time period of the loan.